Generalization of BCS Superconductivity to Non-Phonon Mediated Interactions: The Excitonic Interaction

Abstract

It has long been recognised that, in principle, superconductivity can be induced by mechanisms other than the phonon mechanism. This follows from a simple generalization of the BCS theory, or better the Eliashberg version of that theory, that makes it clear that certain electronic excitations can provide such an attractive interaction. Because of the much higher energies of such excitations, superconductivity at much higher temperatures than those of phonon-mediated superconductors, should be possible. This raises the question whether this mechanism might be responsible for the high-transition temperatures of the recently discovered cuprate superconductors. In considering this question, we discuss the similarities and differences between the phonon mechanism, and such a non-phonon, exciton mechanism, the effects of these upon the superconducting transition temperature, and their effects upon the nature and symmetry of the superconducting state. We discuss the characteristic signature of the non-phonon interaction and review the experimental evidence for and against a possible role such a non-phonon mechanism might play in the superconductivity of the cuprates.